The correspondence between nets and Borchers triples is as follows (see [1]}, [2]}):
If \(({\mathcal {A}}, U, \Omega )\)  is a (two-dimensional) Haag-Kastler net, then \(({\mathcal {A}}(W_{\mathrm {R}}), U|_{{\mathbb {R}}^2}, \Omega )\) 
is a Borchers triple, where \(U\)  is restricted to the translation subgroup \(\cong {\mathbb {R}}^2\) .
